x^4-x^2=47x^2+49

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Solution for x^4-x^2=47x^2+49 equation:


Simplifying
x4 + -1x2 = 47x2 + 49

Reorder the terms:
-1x2 + x4 = 47x2 + 49

Reorder the terms:
-1x2 + x4 = 49 + 47x2

Solving
-1x2 + x4 = 49 + 47x2

Solving for variable 'x'.

Reorder the terms:
-49 + -1x2 + -47x2 + x4 = 49 + 47x2 + -49 + -47x2

Combine like terms: -1x2 + -47x2 = -48x2
-49 + -48x2 + x4 = 49 + 47x2 + -49 + -47x2

Reorder the terms:
-49 + -48x2 + x4 = 49 + -49 + 47x2 + -47x2

Combine like terms: 49 + -49 = 0
-49 + -48x2 + x4 = 0 + 47x2 + -47x2
-49 + -48x2 + x4 = 47x2 + -47x2

Combine like terms: 47x2 + -47x2 = 0
-49 + -48x2 + x4 = 0

Factor a trinomial.
(-1 + -1x2)(49 + -1x2) = 0

Factor a difference between two squares.
(-1 + -1x2)((7 + x)(7 + -1x)) = 0

Subproblem 1

Set the factor '(-1 + -1x2)' equal to zero and attempt to solve: Simplifying -1 + -1x2 = 0 Solving -1 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x2 = 0 + 1 -1x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1x2 = 1 Divide each side by '-1'. x2 = -1 Simplifying x2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7

Subproblem 3

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {-7, 7}

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